Q. The moment of inertia of two spheres of equal masses about their diameters are equal. If one of them is solid and other is hollow, the ratio of their radii is
A) $\sqrt{3}:\sqrt{5}$
B) 3 : 5
C) $\sqrt{5}:\sqrt{3}$
D) 5 : 3
Explanation
(c) $I_{s} = \frac{2}{5}MR_{s}^{2},\ I_{h} = \frac{2}{3}MR_{h}^{2}$
As, $I_{s} = I_{h}$
$\therefore\ \frac{2}{5}MR_{s}^{2} = \frac{2}{3}MR_{h}^{2}$
$\therefore\ \frac{R_{s}}{R_{h}} = \frac{\sqrt{5}}{\sqrt{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.